By a dynamical system we mean a quadruple \((X,B,\mu , T)\) , where \((X,B)\) 
is a standard Borel space, \(\mu \)  is a \(\sigma \) -finite measure on \(B\)  and \(T\)  is an invertible \(\mu \) -preserving transformation of \(X\) .
The dynamical system (or just \(T\) ) is called of rank one if there is a sequence of finite \(T\) -Rokhlin towers that approximates the subring of subsets of finite measure in \(B\) .
There is an alternative (explicit) definition of rank one system via an inductive construction
process of cutting-and-stacking with a single tower on each step.
It is completely determined by two underlying sequences of cuts and spacer mappings.
For details and for the equivalence of various definitions of rank-one we refer to [1]}.
